In the process of machine processing, in order to prevent the tool or the arm from colliding and causing safety problems during the motion of machine processing, an area (usually a cuboid or a cylinder) is specified before transmitting a motion instruction to a machine or a robot, so as to indicate that a trajectory is overtravel when the trajectory exceeds the specified area (in the case that the area is a safe area) or enters the area (in the case that the area is a prohibited area), which is a detection process known as safe area detection.
In the prior art, the trajectory is determined to be within the specified area or outside the specified area through the spatial geometry algorithm directly, in which the presumed conditions are individually made based on different positional relationships between the trajectory and the specified area, and then the determination is performed. Therefore, the algorithm will be quite large, the complexity of the determination of the geometric space relationship will exponentially increases because of the complexity of the geometric shape, and the presumption is likely to miss some possible cases.